Implications of the adding-up condition when estimation is in terms of additive normal errors or additive logistic normal errors is clarified. A byproduct is a parsimonious specification of the autocorrelation matrix with number of parameters equal to number of equations.
McLaren, K. R. (1996). Parsimonious autocorrelation corrections for singular demand systems. Economics Letters, 53(2), 115–121. https://doi.org/10.1016/S0165-1765(96)00915-9